Could someone help?
Does someone have an idea why the start-stop-daemon doesn't find matching processes for my wlan and the lo interface?
Is there a possibility to get more information about it e.g. a log file?

I am not sure why the intefaces reported 'start-stop-daemon: no matching processes found '.
However the syslog-ng most probably failed to stop because the pid file vanished or disappeared somehow or the service wasn't even running (ie. it crashed).

Could you give me the output of 'emerge --info' as well as the version of syslog-ng / openrc and the syslog-ng.conf too.

# The default action of syslog-ng is to log a STATS line
# to the file every 10 minutes. That's pretty ugly after a while.
# Change it to every 12 hours so you get a nice daily update of
# how many messages syslog-ng missed (0).
stats_freq(43200);
# The default action of syslog-ng is to log a MARK line
# to the file every 20 minutes. That's seems high for most
# people so turn it down to once an hour. Set it to zero
# if you don't want the functionality at all.
mark_freq(3600);
};

# ...if you intend to use /dev/console for programs like xconsole
# you can comment out the destination line above that references /dev/tty12
# and uncomment the line below.
#destination console_all { file("/dev/console"); };

Well, all the info you gave seems to be normal.
You should check syslog-ng's internal logs for more details, you'll find them in /var/log/messages. If you still have them from that time when the issue happened.

This will force the service to start in the foreground and redirect every output (even the incoming / outgoing logs, you can omit the '-d' switch if you don't want to include the logs) into a file.
If you got the prompt back immediately then it failed to start.
Try stopping the service by sending a simple kill signal to it. (kill -p $pid)
There should be two syslog-ng processes (pgrep syslog-ng or pidof syslog-ng), the first one is a supervisor process and the other one with bigger pid is the 'working' process. Kill the latter one.

That doesn't show anything suspicious.
As a last idea, you may want to attach an strace to the stuck syslog-ng process (after you treid to stop it) to see what's going on but that's a bit beyond my skills.